[EM] Your votes-only criterion is not equivalent to SDSC.

[MIKE OSSIPOFF]

Markus--

You said:

so far as election methods are defined only on the cast
preferences and not on the sincere preferences, whether a
given election method satisfies a given criterion must be
reflected in the way this method uses the cast preferences.
Therefore, there is no need to include the sincere
preferences in the definition of a criterion.

I reply:

No, that doesn't follow. Yes methods are defined on cast ballots. No, 
criteria needn't be in the form of instructions about how a method uses 
those cast ballots. You've said that you prefer that, and I don't deny that 
you prefer it. But you haven't shown us why a criterion must be in the form 
of an instruction for how a method uses the ballots. A criterion can be 
about something that should or shouldn't happen.

You say that there's no need o mention preferences, meaning presumably that 
it's always possible to write an equivalent criterion that only mentions 
cast ballots, a "votes-onlyl" criterion.

But you didn't succeed in doing so:

Later in your posting you wrote a criterion that you presumably imply is 
equivalent to my SDSC. But it isn't. Plurality meets your criterion. 
Plurality doesn't meet SDSC.

More details about that where this message replies to that part of your 
message.

You said:

I would call

   "If more than half of the voters prefer alternative y over
   alternative x, then that majority must have some way of voting
   that ensures x will not be elected and does not require any of
   them to rank y equal to or over any alternatives preferred over y."

the "motivation" of this criterion and

    "Any ordering of the alternatives must be an admissible vote,
    and if more than half of the voters rank y over x and x no higher
    than tied for bottom, then x must not be elected."

the "definition" of this criterion.

I reply:

You said  "...rank y over x". What if the method isn't a rank method? Or 
does your critrerioin apply only to rank methods? If so, then it isn't 
equivalent to SDSC.

Or maybe when you said "rank y over x", you meant "vote y over X". Of 
course, when writing a criterion, it's better if youi say what you mean. If 
you mean for "rank" to mean "vote", then you've got to tell us what you want 
"rank" to mean.

And you haven't stated a definition for voting y over x anyway.

Maybe you have a definiiton, special for Plurality, that says that if you 
vote for y, then you're "ranking" y over everyoen else. But you didn't tell 
us that, and so, again, your definition isn't complete. Additionallly, if 
that's what you were trying to say, your definitions require a special 
definition for Pluralilty. None of my definitions require a special 
definition for a particular method. Theyi all apply to all proposed methods, 
without method-specific definitions.

So, from the above, your criterion either is unequivalent with SDSC because 
your crirterion applies only to rank methods, or else your definition is 
incompete, and you haven't defined a criterion at all.

But, let's pretend that you've said that you said "vote y over x", and that 
you've specified Richard's or my definition of voting one candidate over 
another, or that you've stated the Plurality-specific definition of ranking 
that I wrote above.  Your criterion still is not equivalent to SDSC. That's 
because now Plurality meets your criterion.

Let me copy your criterion definition here:


    "Any ordering of the alternatives must be an admissible vote,
    and if more than half of the voters rank y over x and x no higher
    than tied for bottom, then x must not be elected."

Say the method is Plurality, and that more than half of the voters vote for 
y. Then x won't win.

Therefore Plurality meets your criterion. Your criterion is not equivalent 
to SDSC.

Your "motivation" says something that roughly resembles the goal of SDSC, 
but your criterion doesn't deliiver what your "motivation" promises.

You really should respect the members of this list enough to check your 
statements before you post them, so that everyone's inbox-space isn't wasted 
with criteria that aren't equivalent to what you want them to be, and my 
demonstrations of that nonequivalence.

Also, maybe you're being a little too ambitious, if you're trying to write 
something equivalent to SDSC.

That's why I suggested that you start with the more familiar Condorcet's 
Criterion.

You didn't write a votes-only critrerion that's equivalent to SDSC.

Can you or can you not write a votes-only criterion that's equivalent to my 
Condorcet's Criterion?

Mike Ossipoff

_________________________________________________________________
Get a FREE online virus check for your PC here, from McAfee. 
http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963